# Neural manifold analysis of brain circuit dynamics in health and disease

arXiv: https://arxiv.org/abs/2203.11874 · HTML: https://mlsanity.com/paper/2203.11874/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Mar 2022.

## Built on by (most cited first, 4 of 4)

- [Exploring Behavior-Relevant and Disentangled Neural Dynamics with Generative Diffusion Models](https://mlsanity.com/paper/2410.09614/) (2024)
- [Extraction and Recovery of Spatio-Temporal Structure in Latent Dynamics Alignment with Diffusion Models](https://mlsanity.com/paper/2306.06138/) (2023)
- [Geometric Properties and Graph-Based Optimization of Neural Networks: Addressing Non-Linearity, Dimensionality, and Scalability](https://mlsanity.com/paper/2503.05761/) (2025)
- [Drift-Diffusion Matching: Embedding dynamics in latent manifolds of asymmetric neural networks](https://mlsanity.com/paper/2602.14885/) (2026)

## Abstract (arXiv)

Recent developments in experimental neuroscience make it possible to simultaneously record the activity of thousands of neurons. However, the development of analysis approaches for such large-scale neural recordings have been slower than those applicable to single-cell experiments. One approach that has gained recent popularity is neural manifold learning. This approach takes advantage of the fact that often, even though neural datasets may be very high dimensional, the dynamics of neural activity tends to traverse a much lower-dimensional space. The topological structures formed by these low-dimensional neural subspaces are referred to as neural manifolds, and may potentially provide insight linking neural circuit dynamics with cognitive function and behavioural performance. In this paper we review a number of linear and non-linear approaches to neural manifold learning, by setting them within a common mathematical framework, and comparing their advantages and disadvantages with respect to their use for neural data analysis. We apply them to a number of datasets from published literature, comparing the manifolds that result from their application to hippocampal place cells, motor cortical neurons during a reaching task, and prefrontal cortical neurons during a multi-behaviour task. We find that in many circumstances linear algorithms produce similar results to non-linear methods, although in particular in cases where the behavioural complexity is greater, nonlinear methods tend to find lower dimensional manifolds, at the possible expense of interpretability. We demonstrate that these methods are applicable to the study of neurological disorders through simulation of a mouse model of Alzheimers Disease, and speculate that neural manifold analysis may help us to understand the circuit-level consequences of molecular and cellular neuropathology.